MULTIPLICITY AND STABILITY OF PREMIXED LAMINAR FLAMES - APPLICATION OF BIFURCATION THEORY

Numerical bifurcation techniques are used to describe multiple steady states for a premixed, laminar flame stabilized on a flat flame burner. The flame is assumed to be adiabatic, and the kinetic mechanism is approximated by a single reaction. The numerical methods make it possible to determine all steady states and eliminate computational difficulties near singular points. The possibility of defining solutions near singularities is particularly important in flame modeling for it is near such points that ignition and burn-out may occur. Three steady states are identified: a stable upper state corresponding to a flame burning at or near the adiabatic flame temperature, a lower solution representing an extinguished stable state, and an unstable intermediate state. Sensitivity of the solutions to changes in kinetic parameters is enhanced near burn-out. It is expected that the ability to predict flame behavior near such singular points will be particularly useful in the determination of flame kinetics. © 1979.